Predictive process monitoring aims to predict future characteristics of an ongoing process case, such as case outcome or remaining time till completion. Several deep learning models have been proposed to address suffix generation and remaining time prediction for ongoing process cases. Though they generally increase the prediction accuracy compared to traditional machine learning models, they still suffer from critical issues. For example, suffixes are generated by training a model on iteratively predicting the next activity. As such, prediction errors are propagated from one prediction step to the next, resulting in poor reliability, i.e., the ground truth and the generated suffixes may easily become dissimilar. Also, conventional training of neural networks via maximum likelihood estimation is prone to overfitting and prevents the model from generating sequences of variable length and with different activity labels. This is an unrealistic simplification as business process cases are often of variable length in reality. To address these shortcomings, this paper proposes an encoder-decoder architecture grounded on Generative Adversarial Networks (GANs), that generates a sequence of activities and their timestamps in an end-to-end way. GANs work well with differentiable data such as images. However, a suffix is a sequence of categorical items. To this end, we use the Gumbel-Softmax distribution to get a differentiable continuous approximation. The training works by putting one neural network against the other in a two-player game (hence the "adversarial" nature), which leads to generating suffixes close to the ground truth. From the experimental evaluation it emerges that the approach is superior to the baselines in terms of the accuracy of the predicted suffixes and corresponding remaining times, despite using a naive feature encoding and only engineering features based on control flow and events completion time.